Question

A light plane attains an airspeed of 480 km/h. The pilot sets out for a destination 780 km due north but discovers that the plane must be headed 19.0

Answer 1

a)

Step 1: Convert the velocities into displacements
Displacement of the plane in two hours = velocity x time = 480 km/hr x 2 hr = 960 km.

The green arrow indicates the direction of wind
AB is the displacement the plane should have followed if there was no wind

Step 2: Use law of cosines to find CB
From law of cosines,
CB² = AB² + AC² - 2 AB. AC .cos
Substituting AB, AC, as 780, 960, 19^o, we get
CB = 337.62 km.
CB is the displacement of the wind in two hours
Velocity = displacement / time = 337.62 / 2 = 168.81 km/hr.

b)

Step 1: Finding the angle ACB
Again by using the law of cosines, we can find the angle,
AB² = CB² + AC² - 2 CB. AC .cos,
Substituting values of AB, CB and AC, we get = 48.7^o.

Step 2: Finding the angle at which the wind is blowing.
Consider the triangle DAC,
angle DAC = 90 + 19 = 109
angle ACD = 48.7
angle ADC = 180 - (109 + 48.7) = 22.3^o.
It is blowing south of west, so it is negative,
Direction is -22.3^o.